Chapter 4.6, Problem 38WE

To determine

To find: the factor of the polynomial $4x^2+3xy-15y^2$ and verify whether it is prime or not.

Answer to Problem 38WE

Yes it is a prime polynomial.

Explanation of Solution

Given information:

Given the polynomial $4x^2+3xy-15y^2$ .

Calculation:

A non-constant polynomial is prime when it cannot factored into non-constant irreducible polynomials.

Multiplying coefficient of $x^2$ and coefficient of $y^2$ that is $4\times 15=60=2\times 2\times 5\times 3$ . Now we cannot express the coefficient of $xy$ that is $3$ in terms oflinear span of $2,2,5,3$ . That implies given polynomial is irreducible and so is a prime polynomial.